Deighton’s Novel. In his World War II historical novel Bomber Len Dieghton argues that a pilot is “mathematically certain” to be shot down in 50 missions if the probability of being shot down on each...

Deighton’s Novel. In his World War II historical novel Bomber Len Dieghton argues that a pilot is “mathematically certain” to be shot down in 50 missions if the probability of being shot down on each mission is 0.02.

(a) Assuming independence of outcomes in each mission, is Deighton’s reasoning correct?

(b) Find the probability of surviving all 50 missions without being shot down?